Monotonicity constraints and supercritical Neumann problems
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 1, p. 63-74

We prove the existence of a positive and radially increasing solution for a semilinear Neumann problem on a ball. No growth conditions are imposed on the nonlinearity. The method introduces monotonicity constraints which simplify the existence of a minimizer for the associated functional. Special care must be employed to establish the validity of the Euler equation.

On démontre l'existence d'une solution positive et radialement croissante pour un problème de Neumann semilinéaire sur une boule. Aucune restriction de croissance n'est imposée sur la nonlinéarité. La méthode indroduit des contraintes de monotonie qui simplifient la preuve de l'existence d'un minimum pour la fonctionnelle associée à l'équation. Une attention particulière est consacrée à la preuve de la validité de l'équation d'Euler.

DOI : https://doi.org/10.1016/j.anihpc.2010.10.003
Classification:  35J60,  58E30
Keywords: Constrained variational problems, Supercritical elliptic equations, Neumann problem
@article{AIHPC_2011__28_1_63_0,
     author = {Serra, Enrico and Tilli, Paolo},
     title = {Monotonicity constraints and supercritical Neumann problems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {28},
     number = {1},
     year = {2011},
     pages = {63-74},
     doi = {10.1016/j.anihpc.2010.10.003},
     zbl = {1209.35044},
     mrnumber = {2765510},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_1_63_0}
}
Serra, Enrico; Tilli, Paolo. Monotonicity constraints and supercritical Neumann problems. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 1, pp. 63-74. doi : 10.1016/j.anihpc.2010.10.003. http://www.numdam.org/item/AIHPC_2011__28_1_63_0/

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